Locality
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The performance of modern computation is characterized by locality of reference, that is, it is cheaper to access data that has been accessed recently than a random piece of data. This is due to many architectural features including caches, lookahead, address translation and the physical properties of a hard disk drive; attempting to model all the components that constitute the performance of a modern machine is impossible, especially for general algorithm design purposes. What if one could prove an algorithm is asymptotically optimal on all systems that reward locality of reference, no matter how it manifests itself within reasonable limits? We show that this is possible, and that algorithms that are asymptotically optimal in the cache-oblivious model are asymptotically optimal in any reasonable locality-of-reference rewarding setting. This is surprising as the cache-oblivious model envisions a particular architectural model involving blocked memory transfer into a multi-level hierarchy of caches of varying sizes, and was not designed to directly model locality-of-reference correlated performance.
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